Finite Group Databasebeta

← Group #10858917

Character table — Group #10858917

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222222222222444444444444444444666688888888888888888888888881212121212121212161616161624242424242424242448
order122222223444466666664444448888121212121212121222224444488121212121212121212122424242424242424444488884121212122244444884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1111-1-111-1-1-1
χ411111111111111111111111111-1-1-1-111111111-1-1-1-1111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1111
χ51111111111111111111111-1-1-1-11111111111111111-1-11-1-111-1-1-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-11-1-1-1-111-1
χ61111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-11-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-11111-1-11
χ71111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1111-1-1-1-11
χ81111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-11111-1
χ911111111111111111111-1-11111111111-1-1-1-1111111-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11111-111-1-1-1-1-11111-1-1-1
χ1011111111111111111111-1-11111111111-1-1-1-111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-111-1-1111-1-1-1-1111
χ1111111111111111111111-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-11-1-111-1-1-1-1-111111
χ1211111111111111111111-1-11111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-11111111-1-11111111-1-1-1-1-1
χ1311111111111111111111-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-111111-1-11111-1-1-1-1-1-1-11
χ1411111111111111111111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-111-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-11-1-111-1-11111111-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-111-1-111-111-1-111-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111-111111111-1-1-1-1-1-1-1-1-1-11111-1-1111111-111-1-1-1-11-1-111-1-11
χ17222222222-2-2-2-222222222200000000-2-22222-2-2222200-200000000-2-2000000000000-2-22200000000000-20000000
χ18222222222-2-2-2-222222222200000000-2-22222-2-2-2-2-2-200-200000000-2-200000000000022-2-20000000000020000000
χ19222222222-2-2-2-22222222-2-200000000-2-2-2-2-2-2-2-222220020000000022000000000000-2-2-2-20000000000020000000
χ20222222222-2-2-2-22222222-2-200000000-2-2-2-2-2-2-2-2-2-2-2-20020000000022000000000000222200000000000-20000000
χ2122222222-12222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-100002222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000002-1-1-1-10000000000
χ2222222222-12222-1-1-1-1-1-1-1222222-2-2-2-2-1-1-1-1-1-1-1-10000222-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111100000000-211110000000000
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-22222-1-1-1-1-1-1-1-10000-2-22-2-2221111-1-11111-1-1-1-1-1-1-1-100000000-211110000000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-10000-2-2222-2-21111-1-1111111111111000000002-1-1-1-10000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-222222222-1-11111-1-10000-2-2-222-2-2111111-1-1-1-1-1-1-1-1111100000000-2-1-1110000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-22222-2-2-2-2-1-11111-1-10000-2-2-2-2-222111111-1-1-1-11111-1-1-1-100000000211-1-10000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-22222-1-11111-1-1000022-2-2-2-2-2-1-1-1-1111111-1-1-1-1111100000000211-1-10000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-2-1-11111-1-1000022-22222-1-1-1-11111111111-1-1-1-100000000-2-1-1110000000000
χ29222-22-2-2-2222-2-22-22-22-2-20000000000220000-2-222-2-22-20000022-2-2000000000000002-2000000000002-200000000
χ30222-22-2-2-2222-2-22-22-22-2-20000000000220000-2-222-2-2-2200000-2-222000000000000002-200000000000-2200000000
χ31222-22-2-2-2222-2-22-22-22-2-20000000000220000-2-2-2-2222-20000022-2-200000000000000-2200000000000-2200000000
χ32222-22-2-2-2222-2-22-22-22-2-20000000000220000-2-2-2-222-2200000-2-22200000000000000-22000000000002-200000000
χ33222-22-2-2-22-2-2222-22-22-2-2002i2i−2i−2i0000-2-200002222-2-200000000000002i2i−2i−2i00000000-2200000000000000002i−2i000
χ34222-22-2-2-22-2-2222-22-22-2-2002i2i−2i−2i0000-2-2000022-2-22200000000000002i2i−2i−2i000000002-20000000000000000−2i2i000
χ35222-22-2-2-22-2-2222-22-22-2-200−2i−2i2i2i0000-2-200002222-2-20000000000000−2i−2i2i2i00000000-220000000000000000−2i2i000
χ36222-22-2-2-22-2-2222-22-22-2-200−2i−2i2i2i0000-2-2000022-2-2220000000000000−2i−2i2i2i000000002-200000000000000002i−2i000
χ372-222-2-22-220000-22-2-222-22i−2i0000−i2−i2i2i2002i2i−2i−2i002-22-2000002−20000000000−i2−i2i2i222−2−2002i−2i−i2−i2i2i20000000000002−20
χ382-222-2-22-220000-22-2-222-22i−2i0000−i2−i2i2i2002i2i−2i−2i00-22-22000002−20000000000−i2−i2i2i222−2−200−2i2ii2i2−i2−i2000000000000−220
χ392-222-2-22-220000-22-2-222-22i−2i0000i2i2−i2−i2002i2i−2i−2i002-22-200000−220000000000i2i2−i2−i2−2−222002i−2ii2i2−i2−i2000000000000−220
χ402-222-2-22-220000-22-2-222-22i−2i0000i2i2−i2−i2002i2i−2i−2i00-22-2200000−220000000000i2i2−i2−i2−2−22200−2i2i−i2−i2i2i20000000000002−20
χ412-222-2-22-220000-22-2-222-2−2i2i0000−i2−i2i2i200−2i−2i2i2i002-22-200000−220000000000−i2−i2i2i2−2−22200−2i2i−i2−i2i2i2000000000000−220
χ422-222-2-22-220000-22-2-222-2−2i2i0000−i2−i2i2i200−2i−2i2i2i00-22-2200000−220000000000−i2−i2i2i2−2−222002i−2ii2i2−i2−i20000000000002−20
χ432-222-2-22-220000-22-2-222-2−2i2i0000i2i2−i2−i200−2i−2i2i2i002-22-2000002−20000000000i2i2−i2−i222−2−200−2i2ii2i2−i2−i20000000000002−20
χ442-222-2-22-220000-22-2-222-2−2i2i0000i2i2−i2−i200−2i−2i2i2i00-22-22000002−20000000000i2i2−i2−i222−2−2002i−2i−i2−i2i2i2000000000000−220
χ452-2-222-2-2222-22-2-222-2-2-22002-22-22i−2i2i−2i2-200002-200000002i−2i000000002-22-22i−2i2i−2i00000000000002i−2i000000000000
χ462-2-222-2-2222-22-2-222-2-2-22002-22-2−2i2i−2i2i2-200002-20000000−2i2i000000002-22-2−2i2i−2i2i0000000000000−2i2i000000000000
χ472-2-222-2-2222-22-2-222-2-2-2200-22-222i−2i2i−2i2-200002-20000000−2i2i00000000-22-222i−2i2i−2i0000000000000−2i2i000000000000
χ482-2-222-2-2222-22-2-222-2-2-2200-22-22−2i2i−2i2i2-200002-200000002i−2i00000000-22-22−2i2i−2i2i00000000000002i−2i000000000000
χ492-2-222-2-22-12-22-21-1-1111-1002-22-22i−2i2i−2i-113−33−3-1100000002i−2i003−33−33−3-11-11−ii−ii−i3i3−i3i3000000000−ii−i3i30000000000
χ502-2-222-2-22-12-22-21-1-1111-1002-22-22i−2i2i−2i-11−33−33-1100000002i−2i00−33−33−33-11-11−ii−iii3−i3i3−i3000000000−iii3−i30000000000
χ512-2-222-2-22-12-22-21-1-1111-1002-22-2−2i2i−2i2i-113−33−3-110000000−2i2i003−33−33−3-11-11i−ii−ii3−i3i3−i3000000000i−ii3−i30000000000
χ522-2-222-2-22-12-22-21-1-1111-1002-22-2−2i2i−2i2i-11−33−33-110000000−2i2i00−33−33−33-11-11i−ii−i−i3i3−i3i3000000000i−i−i3i30000000000
χ532-2-222-2-22-12-22-21-1-1111-100-22-222i−2i2i−2i-113−33−3-110000000−2i2i00−33−333−31-11-1−ii−ii−i3i3−i3i3000000000i−ii3−i30000000000
χ542-2-222-2-22-12-22-21-1-1111-100-22-222i−2i2i−2i-11−33−33-110000000−2i2i003−33−3−331-11-1−ii−iii3−i3i3−i3000000000i−i−i3i30000000000
χ552-2-222-2-22-12-22-21-1-1111-100-22-22−2i2i−2i2i-113−33−3-1100000002i−2i00−33−333−31-11-1i−ii−ii3−i3i3−i3000000000−ii−i3i30000000000
χ562-2-222-2-22-12-22-21-1-1111-100-22-22−2i2i−2i2i-11−33−33-1100000002i−2i003−33−3−331-11-1i−ii−i−i3i3−i3i3000000000−iii3−i30000000000
χ572-2-2-2222-22-222-2-2-222-22-2002i−2i−2i2i0000-2200002-2000000000000000002i−2i−2i2i0000000000002i−2i2i−2i000000002-200000
χ582-2-2-2222-22-222-2-2-222-22-2002i−2i−2i2i0000-2200002-2000000000000000002i−2i−2i2i000000000000−2i2i−2i2i00000000-2200000
χ592-2-2-2222-22-222-2-2-222-22-200−2i2i2i−2i0000-2200002-200000000000000000−2i2i2i−2i0000000000002i−2i2i−2i00000000-2200000
χ602-2-2-2222-22-222-2-2-222-22-200−2i2i2i−2i0000-2200002-200000000000000000−2i2i2i−2i000000000000−2i2i−2i2i000000002-200000
χ6144444444-2-4-4-4-4-2-2-2-2-2-2-2440000000022-2-2-2-222000000-4000000002200000000000000000000000000000000000
χ6244444444-2-4-4-4-4-2-2-2-2-2-2-2-4-40000000022222222000000400000000-2-200000000000000000000000000000000000
χ63444-44-4-4-4-244-4-4-22-22-2220000000000-2-200002200004-400000-2-2220000000000000000000000000000000000000
χ64444-44-4-4-4-244-4-4-22-22-2220000000000-2-20000220000-440000022-2-20000000000000000000000000000000000000
χ65444-44-4-4-4-2-4-444-22-22-222004i4i−4i−4i0000220000-2-200000000000000000−2i−2i2i2i0000000000000000000000000000000
χ66444-44-4-4-4-2-4-444-22-22-22200−4i−4i4i4i0000220000-2-2000000000000000002i2i−2i−2i0000000000000000000000000000000
χ6744-44-44-4-44000044-44-4-4-400000022−22−22220000000000000000000000000000022−22−2222000000000000000000000000000
χ6844-44-44-4-44000044-44-4-4-4000000−222222−2200000000000000000000000000000−222222−22000000000000000000000000000
χ6944-44-44-4-4-20000-2-22-222200000022−22−222200−2i32i32i3−2i300000000000000000000000−222−2i6−i6−i6i600000000000000000000000
χ7044-44-44-4-4-20000-2-22-222200000022−22−2222002i3−2i3−2i32i300000000000000000000000−222−2−i6i6i6−i600000000000000000000000
χ7144-44-44-4-4-20000-2-22-2222000000−222222−2200−2i32i32i3−2i3000000000000000000000002−2−22−i6i6i6−i600000000000000000000000
χ7244-44-44-4-4-20000-2-22-2222000000−222222−22002i3−2i3−2i32i3000000000000000000000002−2−22i6−i6−i6i600000000000000000000000
χ7344-4-4-4-444400004-4-4-4-44400000000000000000000000000000000000000000000000000022−22−2222000000000000000
χ7444-4-4-4-444400004-4-4-4-444000000000000000000000000000000000000000000000000000−222222−22000000000000000
χ754-444-4-44-4-200002-222-2-224i−4i0000−2i2−2i22i22i200−2i−2i2i2i0000000000022−220000000000i2i2−i2−i2−2−22200000000000000000000000
χ764-444-4-44-4-200002-222-2-224i−4i00002i22i2−2i2−2i200−2i−2i2i2i00000000000−22220000000000−i2−i2i2i222−2−200000000000000000000000
χ774-444-4-44-4-200002-222-2-22−4i4i0000−2i2−2i22i22i2002i2i−2i−2i00000000000−22220000000000i2i2−i2−i222−2−200000000000000000000000
χ784-444-4-44-4-200002-222-2-22−4i4i00002i22i2−2i2−2i2002i2i−2i−2i0000000000022−220000000000−i2−i2i2i2−2−22200000000000000000000000
χ794-44-4-44-4440000-4-4-444-440000000000000000004-4-44000000000000000000000000000000000000000000000000
χ804-44-4-44-4440000-4-4-444-44000000000000000000-444-4000000000000000000000000000000000000000000000000
χ814-4-444-4-444-44-44-444-4-4-440000000000-440000-440000000000000000000000000000000000000000000000000000
χ824-4-444-4-44-2-44-442-2-2222-200000000002-223−2323−232-2000000000000000−232300000000000000000000000000000000000
χ834-4-444-4-44-2-44-442-2-2222-200000000002-2−2323−23232-200000000000000023−2300000000000000000000000000000000000
χ844-4-4-4444-444-4-44-4-444-44-400000000004-40000-440000000000000000000000000000000000000000000000000000
χ854-4-4-4444-4-24-4-4422-2-22-220000000000-2200002-20000000000023−23−23230000000000000000000000000000000000000
χ864-4-4-4444-4-24-4-4422-2-22-220000000000-2200002-200000000000−232323−230000000000000000000000000000000000000
χ874-4-4-4444-4-2-444-422-2-22-22004i−4i−4i4i00002-20000-2200000000000000000−2i2i2i−2i0000000000000000000000000000000
χ884-4-4-4444-4-2-444-422-2-22-2200−4i4i4i−4i00002-20000-22000000000000000002i−2i−2i2i0000000000000000000000000000000
χ8988-8-8-8-888-40000-44444-4-40000000000000000000000000000000000000000000000000000000000000000000000
χ908-88-8-88-88-40000444-4-44-40000000000000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).